Add all of the patty ingredients to a bowl and mix to combine.
Divide the mixture into 4. Roll each quarter into a ball and then flatten into a burger patty, leaving an indent in the center so the burger cooks flat instead of puffing up.
Heat a grill pan over medium or medium-high heat. Add the patties and cook for 5-7 minutes per side or until cooked through, until they reach an internal temperature of 160°F (71°C).
Add the shredded cheese in mounds on top of the patties. Stream in a tablespoon or two of water to the center of the pan and quickly add a lid. Let the cheese steam for a minute or two to melt. Set the patties aside on a plate.
Add the buns to the grill pan to toast for 2-4 minutes.
For the sauce
Add the yogurt, mayo, and milk in a bowl and whisk until smooth.
Add the rest of the ingredients and mix to combine.
For the burger
Add sauce to the bottom bun. Add the cheesy patty, followed by pickled jalapeño slices (if using), and shredded lettuce. Add sauce to the top bun and add it to the burger to close. Serve.
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Notes
The sauce makes 1 cup, which is about double what you'll need if you use 2 tablespoons per burger, which is the amount in the nutrition estimate.For juicy burgers avoid pressing down on them with a spatula or poking them open. This releases their moisture and can result in dry burgers.Control the heat level by adding more or less jalapeño to your burger. You can add chopped fresh or pickled jalapeños to the patty mixture for a spicier burger.The nutrition estimate doesn't include buns, as that can vary greatly.Nutritional yeast gives a 'cheesy' kind of feeling to this ranch dressing. A lot of store-bought ranch dressings contain buttermilk powder for flavor.